The confusion table that resulted from classifying the mails with our naive bayes classifier can be seen in table \ref{tab:conf}. These are the results with the final features we chose. This classification gives us a failure rate of roughly 88\% which we consider quite good. The biggest flaw in this implementation is that still too much ham mails get classified as spam. 

\begin{table}
\centering
\begin{tabular}{|c|c|}
\hline
true positives & false positives\\
\hline
41 & 13\\
133 & 11\\
\hline
true negatives & false negatives\\
\hline
\end{tabular}
\caption{Confusion matrix of our bayesian classifier}
\label{tab:conf}
\end{table}

To get better results, given the categorization of ham mails as spam we set a threshold as described in section \ref{sec:threshold}. When experimenting with this threshold we focused on the wrongful categorization of ham mails into spam, because this is the situation which should occur less often.
after testing with values from 0.2 to 0.001 we found that the best value seems to be 0.005 since then only 3 mails get classified as spam which should be ham. Therefore 26 of the spam mails come through which is roughly half of the testes spam mails. This is still suboptimal since it it still a very large number but for this the regexp conditions could be updated to even more powerful regulations. In real mail situations one thing to consider is also the factor that ip addresses can be included, which give a filter more control over the possibility of spam mail than exists by purely analyzing the content of the spam.
